Unit 2 Practice Free Response Question Solution and Rubric
Solution:
(a) ŷ = −4702.64 + 21.282x where ŷ is the predicted fuel consumed, in pounds, and x is the distance,
in miles.
(b) The linear regression model is appropriate in this setting because the residual plot shows no
discernable pattern.
(c) The y-intercept of -4702.64 means that a plane traveling zero miles would be predicted to
consume negative 4702.64 pounds of fuel. Since a plane would not have a flight covering zero miles,
this number is not statistically meaningful.
Scoring:
Part (a) is graded as essentially correct (E), partially correct (P), or incorrect (I)
Essentially correct if:
The regression equation is correct.
AND
The variables ŷ and x are defined, including units.
Note: it is acceptable to define y as long as the regression equation is written in terms of ŷ .
Partially correct if:
1. The regression equation is correct but the variable definitions are incorrect or missing.
OR
2. The regression equation and variables are defined correctly, but the equation is written in terms of
y instead of ŷ .
Incorrect in all other cases.
Part (b) is graded as essentially correct (E), partially correct (P), or incorrect (I)
Essentially correct if
It is mentioned that the linear regression model is appropriate because the residual plot shows no
pattern.
Partially correct if
It is mentioned that the linear regression model is appropriate because of the residual plot, but it is
unclear or omitted what property of the residual plot is important.
Incorrect in all other cases.
Note: Using r2 as the reason the linear model is appropriate is not an acceptable justification.
Part (c) is graded as essentially correct (E), partially correct (P), or incorrect (I)
Essentially correct if
The y-intercept is interpreted as the predicted amount of fuel consumed on a zero mile flight.
AND
It is mentioned that this value is not meaningful because a zero mile flight does not make sense or that
consuming negative fuel does not make sense.
Partially correct if
One of the two parts is correct.
Incorrect in all other cases.
Note: If the incorrect y-intercept is identified in part (a), the student can still earn an essentially correct
(E) in part (c) if the interpretation and meaningfulness are correct for the y-intercept identified in part (a).
4
Complete Response
Three parts essentially correct
3
Substantial Response
Two parts essentially correct and one part partially correct
2
Developing Response
Two parts essentially correct and one part incorrect
One part essentially correct and two parts partially correct
One part essentially correct and one part partially correct
Three parts partially correct
1
Minimal Response
One part essentially correct and two parts incorrect
Two parts partially correct and one part incorrect